Being lightweight, yet capable of producing high energy densities, lithium secondary batteries are preferably used as so-called portable batteries for PCs and mobile devices, etc., and vehicle-installed batteries. In particular, great importance is placed on them as high-power batteries for driving vehicles such as electric automobiles, hybrid automobiles and the like. In such lithium secondary batteries, it has been suggested to add a cyclic siloxane to non-aqueous electrolyte solutions to increase their cycle characteristics. Literatures disclosing this type of conventional art include Patent Documents 1 to 4.